Don't just start replacing every part.
Concentrate on the cause of the problem.
" all that happens is just the solenoid clicking. "
The solenoid is making a noise because of low voltage. That is likely caused by:
1. A weak battery (charge it & check it per tip # 49))
2. Dirty grounds/connections (remove the cables & clean the connections)
3. Bad cables or incorrect sized cables (replace them - see tip # 41)
4. Bad ground between the starter & the block. (pull the starter away from the block & clean the mating area - see tip # 36)
" At his point I have cleaned and checked the cables ..."
You do not have x-ray vision. You can not see corrosion in the cables.